Vol. 56, No. 2, 1975

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Continuité du spectre dans les algèbres de Banach avec involution

B. Aupetit

Vol. 56 (1975), No. 2, 321–324
Abstract

Let A a complex Banach algebra with an involution. If the spectral radius is submultiplicative on the set of hermitian elements the spectrum is continuous on the set of normal elements. From this we conclude that the set of hermitian elements with real spectrum is closed in the set of hermitian elements, which generalizes a result of B. Yood.

Mathematical Subject Classification 2000
Primary: 46K05
Milestones
Received: 26 November 1973
Revised: 21 May 1974
Published: 1 February 1975
Authors
B. Aupetit